I'm pretty sure Percy is saying that the A/T will not do anything (as your books say)
Well, if you are now speaking for Percy, then maybe you can explain how the A/T can "remain[] armed throughout" but the "A/T will not do anything."
My books don't address this issue, as I'm sure yours don't either or you would have an answer.
To simplify the question: If you do a manual landing with the A/T engaged and you
do not use reverse, will the A/T attempt to maintain the MCP speed on rollout? According to Percy, if the A/T is armed, then when the speed starts to bleed off on the rollout the A/T will advance power to maintain the MCP speed.